code: def test_rewriting():
      from sympy.functions.elementary.piecewise import Piecewise
  
      assert isinstance(dirichlet_eta(x).rewrite(zeta), Piecewise)
      assert isinstance(dirichlet_eta(x).rewrite(genocchi), Piecewise)
      assert zeta(x).rewrite(dirichlet_eta) == dirichlet_eta(x) / (
          1 - 2 ** (1 - x)
      )
      assert zeta(x).rewrite(dirichlet_eta, a=2) == zeta(x)
      assert verify_numerically(
          dirichlet_eta(x), dirichlet_eta(x).rewrite(zeta), x
      )
      assert verify_numerically(
          dirichlet_eta(x), dirichlet_eta(x).rewrite(genocchi), x
      )
      assert verify_numerically(
          zeta(x), zeta(x).rewrite(dirichlet_eta), x
      )
  
      assert zeta(x, a).rewrite(lerchphi) == lerchphi(1, x, a)
      assert polylog(s, z).rewrite(lerchphi) == lerchphi(z, s, 1) * z
  
      assert lerchphi(1, x, a).rewrite(zeta) == zeta(x, a)
      assert z * lerchphi(z, s, 1).rewrite(polylog) == polylog(s, z)
  
imports: from sympy.concrete.summations import Sum
  from sympy.core.function import expand_func
  from sympy.core.numbers import Float, I, Rational, nan, oo, pi, zoo
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.elementary.complexes import Abs, polar_lift
  from sympy.functions.elementary.exponential import exp, exp_polar, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.special.zeta_functions import dirichlet_eta, lerchphi, polylog, riemann_xi, stieltjes, zeta
  from sympy.series.order import O
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic
  from sympy.testing.pytest import raises
  from sympy.core.random import test_derivative_numerically, random_complex_number, verify_numerically
label_desc: Use image node_id 5 for calling a global function with example usage: test_rewriting() without return types